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In a typical decentralized group planning algorithm, each robot might broadcast its observations of the environment to its teammates, and all the robots would then execute the same planning algorithm, presumably on the basis of the same information.
But Rus, Alonso-Mora, and their colleagues found a way to reduce both the computational and communication burdens imposed by consensual planning. The essential idea is that each robot, on the basis of its own observations, maps out an obstacle-free region in its immediate environment and passes that map only to its nearest neighbors. When a robot receives a map from a neighbor, it calculates the intersection of that map with its own and passes that on.
This keeps down both the size of the robots’ communications — describing the intersection of 100 maps requires no more data than describing the intersection of two — and their number, because each robot communicates only with its neighbors. Nonetheless, each robot ends up with a map that reflects all of the obstacles detected by all the team members.
Four dimensions
The maps have not three dimensions, however, but four — the fourth being time. This is how the algorithm accounts for moving obstacles. The four-dimensional map describes how a three-dimensional map would have to change to accommodate the obstacle’s change of location, over a span of a few seconds. But it does so in a mathematically compact manner.
The algorithm does assume that moving obstacles have constant velocity, which will not always be the case in the real world. But each robot updates its map several times a second, a short enough span of time that the velocity of an accelerating object is unlikely to change dramatically.
On the basis of its latest map, each robot calculates the trajectory that will maximize both its local goal — staying in formation — and its global goal.
The researchers are also testing a version of their algorithm on wheeled robots whose goal is to collectively carry an object across a room where human beings are also moving around, as a simulation of an environment in which humans and robots work together.
